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We now want to consider the length of the path the light traverses in the clock from the point of view of an observer in reference frame S. One expression for the length of this path is simply. Lg-tgc/2-that is, the length of the path is simply the distance that light travels in one half-tick. Use geometry to find another expression for the length of a one-way trip Ls (eg, from the source to the top mirror) according to this observer. Express your answer in terms of the time ts, v, and L.

We now want to consider the length of the path the light traverses in the clock from the point of view of an observer in reference frame S. One expression for the length of this path is simply. Lg-tgc/2-that is, the length of the path is simply the distance that light travels in one half-tick. Use geometry to find another expression for the length of a one-way trip Ls (eg, from the source to the top mirror) according to this observer. Express your answer in terms of the time ts, v, and L.

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rkbook Sharing S In this problem, we consider a light clock-a clock that ticks every time light makes a round trip between two mirrors separated by a distance L. The key point is that we can deduce the rate at which this clock ticks, when it moves relative to us as well as when it is at rest, directly from the postulates of special relativity. The postulates of special relativity are as follows: 1. The laws of physics are the same in any coordinate system that moves at constant velocity (i.e., any inertial reference frame). 2. The speed of light is c when measured with respect to any coordinate system moving at a constant velocity. As shown in the figure (Eigure 1), the light clock is based on the propagation time of light between mirrors spaced a distance L apart (in the rest frame of the clock). As the light bounces back and forth between the mirrors, a small bit of light is allowed to escape through the partially silvered lower mirtor. These transmitted pulses of light hit a detector, which therefore emits evenly spaced (in time) "ticks each round-trip time of the pulse. (New pulses are injected in phase with the detected pulses to keep the clock going.) Figure Light Clock Pulses each fo < 1 of 2 > Part C We now want to consider the length of the path the light traverses in the clock from the point of view of an observer in reference frame S. One expression for the length of this path is simply: Ls=tsc/2-that is, the length of the path is simply the distance that light travels in one half-tick. Use geometry to find another expression for the length of a one-way trip Lg (eg, from the source to the top mirror) according to this observer. Express your answer in terms of the time ts, v, and L. ►View Available Hint(s) VE ΑΣΦ Lg= Submit Part D What is the time ts between the ticks of the light clock as viewed from reference frame S? Express the time of these ticks in terms of to (the ticks in the frame of the clock), the relative speed u, and the speed of light c. ► View Available Hint(s) ts= Submit ? 15] ΑΣΦ/Φ ?
Transcribed Image Text:rkbook Sharing S In this problem, we consider a light clock-a clock that ticks every time light makes a round trip between two mirrors separated by a distance L. The key point is that we can deduce the rate at which this clock ticks, when it moves relative to us as well as when it is at rest, directly from the postulates of special relativity. The postulates of special relativity are as follows: 1. The laws of physics are the same in any coordinate system that moves at constant velocity (i.e., any inertial reference frame). 2. The speed of light is c when measured with respect to any coordinate system moving at a constant velocity. As shown in the figure (Eigure 1), the light clock is based on the propagation time of light between mirrors spaced a distance L apart (in the rest frame of the clock). As the light bounces back and forth between the mirrors, a small bit of light is allowed to escape through the partially silvered lower mirtor. These transmitted pulses of light hit a detector, which therefore emits evenly spaced (in time) "ticks each round-trip time of the pulse. (New pulses are injected in phase with the detected pulses to keep the clock going.) Figure Light Clock Pulses each fo < 1 of 2 > Part C We now want to consider the length of the path the light traverses in the clock from the point of view of an observer in reference frame S. One expression for the length of this path is simply: Ls=tsc/2-that is, the length of the path is simply the distance that light travels in one half-tick. Use geometry to find another expression for the length of a one-way trip Lg (eg, from the source to the top mirror) according to this observer. Express your answer in terms of the time ts, v, and L. ►View Available Hint(s) VE ΑΣΦ Lg= Submit Part D What is the time ts between the ticks of the light clock as viewed from reference frame S? Express the time of these ticks in terms of to (the ticks in the frame of the clock), the relative speed u, and the speed of light c. ► View Available Hint(s) ts= Submit ? 15] ΑΣΦ/Φ ?
the pulse. (New pulses are injected in phase with the detected pulses to keep the clock going.) Figure 1 T L V -d 12 10 < 2 of 2 4 Pro
Transcribed Image Text:the pulse. (New pulses are injected in phase with the detected pulses to keep the clock going.) Figure 1 T L V -d 12 10 < 2 of 2 4 Pro
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